BabylonianMathematics 15
their priests. Writing of the most basic kind was developed around 3300bce, and continued using a
more developed form of the original ‘cuneiform’ (wedge-shaped) script for 3000 years, in different
languages. The documents have been unusually well preserved because the texts were produced by
making impressions on clay tablets, which hardened quickly and were preserved even when thrown
away orused as rubble to fill walls (see Fig. 1). A relatively short period in the long history has
provided the main mathematical documents, as far as our present knowledge goes. As usual, we
should be careful; our knowledge and estimation of the field has changed over the past 30 years and
we have no way of knowing (a) what future excavation or decipherment will turn up and (b) what
texts, currently ignored, will be found important by future researchers. In this period—from 2500
to 1750bce—the Sumerians, founders of a south Iraqi civilization based on Uruk, and inventors of
writing among other things—were overthrown by a Semitic-speaking people, the Akkadians, who
as invaders often do, adopted the Sumerian model of the state and used Sumerian (which is not
related to any known language, and which gradually became extinct) as the language of culture.
A rough guide will show the periods from which our main information on mathematics derives:
2500 bce‘Fara period’. The earliest (Sumerian) school texts, from Fara near Uruk; beginning of
phonetic writing.
2340 bce‘Akkadian dynasty’. Unification of all Mesopotamia under Sargon (an Akkadian).
Cuneiform is adapted to write in Akkadian; number system further developed.
2100 bce‘Ur III’. Re-establishment of Ur, an ancient Sumerian city, as capital. Population now
mixed, with Akkadians in the majority. High point of bureaucracy under King Šulgi.
1800 bce‘Old Babylonian’, or OB. Supremacy of the northern city of Babylon under (Akkadian)
Hammurapi and his dynasty. The most sophisticated mathematical texts.
MS 1844
Fig. 1A mathematical tablet (Powers of 70 multiplied by 2. Sumer, C. 2050 BC).